Finite-volume excitations of the 111 interface in the quantum XXZ model

TL;DR

This paper investigates localized excitations at the 111 interface in the 3D XXZ ferromagnet, establishing bounds on their energies and proving ensemble equivalence for interface states in the thermodynamic limit.

Contribution

It introduces a rigorous analysis of interface excitations in the XXZ model and proves ensemble equivalence for fixed and fluctuating magnetization states.

Findings

Excitations localized in a subvolume have energies bounded by O(1/R^2)

Ensemble equivalence holds for interface states in the thermodynamic limit

Convergence of canonical states with fixed magnetization is established

Abstract

We show that the ground states of the three-dimensional XXZ Heisenberg ferromagnet with a 111 interface have excitations localized in a subvolume of linear size R with energies bounded by O(1/R^2). As part of the proof we show the equivalence of ensembles for the 111 interface states in the following sense: In the thermodynamic limit the states with fixed magnetization yield the same expectation values for gauge invariant local observables as a suitable grand canonical state with fluctuating magnetization. Here, gauge invariant means commuting with the total third component of the spin, which is a conserved quantity of the Hamiltonian. As a corollary of equivalence of ensembles we also prove the convergence of the thermodynamic limit of sequences of canonical states (i.e., with fixed magnetization).